> -> Sets^{op}. While it gi=
ves the correct objects, the morphisms=C2=A0
> C -&=
gt; Sets^{op} but in the opposite category.
Ah, ri=
ght. =C2=A0The reason why I defined presheaves this way is that=C2=A0
=
you can just say that the slice category over a presheaf $P$ is=C2=A0<=
/div>
presheaves over the category of elements of $P$, rather than=C2=
=A0
copresheaves, so it's more uniform and certain proofs bec=
ome a=C2=A0
little bit nicer. =C2=A0Of course, one could start wi=
th C^{op} and use=C2=A0
copresheaves throughout, but then I think=
things would get quite=C2=A0
confusing with the Yoneda embedding=
.
But thanks for pointing out this problem. =C2=A0=
Somehow, it had never=C2=A0
occured to me that natural transforma=
tions are going in the wrong=C2=A0
direction with my definition.<=
/div>
Paolo
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